A large class of information signals, including speech, television, and imagery are analog in nature and must be sampled and quantized for digital storage or transmission. One common technique for digitizing the analog information is to sample it and encode the results using pulse code modulation (PCM). Pulse code modulation (PCM) is the most prevalent method of converting analog information to digital pulses. The analog voltage is sampled at regular intervals by a sample-and-hold circuit and, while this sampled value of voltage is held constant, an analog-to-digital converter converts it to a binary number. This number is proportional to the amplitude of the analog signal at the time of sampling. The binary equivalent of the sampled voltage level is transmitted and reconverted at the receive end to a voltage level by a digital-to-analog converter.
The Nyquist sampling theorem states that a bandlimited analog information signal can be digitized using PCM (and later recovered) by sampling at a rate R, if R is two or more times the maximum information signal frequency or bandwidth. If this condition is satisfied, the analog information signal can be completely recovered, at the receiving end for example, by passing the PCM signal through a digital-to-analog converter and an ideal low pass filter with a cutoff frequency equal to the maximum information signal frequency or information signal bandwidth.
Thus, the Nyquist sampling theorem states that there is a minimum rate (equal to twice the information bandwidth) at which a signal can be sampled and for which theoretically exact reconstruction of the signal is possible from its samples. If an information signal is sampled below this minimum rate, distortions in the form of spectral foldover or aliasing occur and the information signal is not recoverable. To ensure that the conditions of the sampling theorem are met for a given application, the information signal to be sampled is generally first filtered by a lowpass filter having a cutoff frequency less than (or equal to) half the sampling frequency. These lowpass filters are sometimes referred to as Nyquist filters or as brick-wall filters because of their sharp cutoff characteristics.
While PCM coding applies to the digitization of analog signals, the Nyquist sampling theorem can be applied to both analog and digital signals. A digital signal that has been bandlimited can be reconstructed by sampling at the data rate R, if the digital signal has been bandlimited to a spectrum of R/2. Digital terrestial microwave link signals are typically bandlimited in this manner to conserve link bandwidth and are thus reconstructed at the receiving end by sampling at the bit rate R.
FIG. 1 illustrates a received digital information signal that is to be sampled for detection. The reference characters 10, 12, 14, and 16 indicate the time at which each bit interval is sampled to determine its logic level. The times 10, 12, 14, and 16 are established by a clock signal at the receiving end., the clock signal is typically derived from the received information signal. If the information signal of FIG. 1 is first band limited, for example to conserve transmission bandwidth, the step transition between the zero bit and the one bit is rounded. Depending on the bandwidth of the bandlimiting filter, the transition between the zero bit and the one bit may be changed by the filtering action to a transition represented by the dashed line between sampling time 12 and sampling time 14. Now the bandlimited signal lacks a well defined step, complicating clock recovery, and thus detection. In fact, the dashed line transition of FIG. 1 represents the optimum bandwidth constraint on the information signal. For example, if the signal reaches the one logic level prior to the sampling time 14 the signal occupies an excess of amount of bandwidth, which is objectionable from a communications link bandwidth perspective. Likewise, if the transition between the sampling times 12 and 14 reaches the one logic level after the sampling time 14 then the data cannot be properly sampled for detection because the occupied bandwidth is too narrow.
lined transition of FIG. 1 represents the optimum transition, as created by bandlimiting filter action, to ensure that a minimum bandwidth is occupied while allowing the sampling action to occur immediately after the information signal has reached a new logic level.
FIG. 2 illustrates, in a different way, the problems associated with limiting the information signal to an overly restrictive bandwidth. In this case the transitions are so severely distorted by bandlimiting, as illustrated by the dashed line, that there is not sufficient time for the information signal to reach the logic level. If the sampling occurs at the sampling times designated by reference character 10, 12, 14, and 16, the logic level at those times may be incorrect and the sampled result will also be wrong. This phenomenon, where the signal does not reach the logic level at the correct time, is known as intersymbol interference.
The key to accurate data detection at the receiving end is accurate clock recovery. If the sampling clock pulse occurs at the midpoint of each received bit interval the likelihood of accurate detection is maximized and the bit-error rate is minimized. If the information signal has not been bandlimited, i.e., is a wideband information, there are several well known clock recovery techniques that can be used. Among these techniques are a nonlinear-filter synchronizer, which is an open loop synchronizer that linearly filters the received bit stream to reduce the noise and magnify the observability of the bit transitions. The filter output is then passed through a memory-less even-law nonlinearity to produce a spectral line at the bit rate. Two closed loop type clock recovery schemes for wideband data are the in phase/midphase synchronizer and the early-late bit synchronizer. The optimum (maximum-likelihood) synchronizer is also a wideband clock recovery scheme that uses an optimal means for searching for the correct synchronization time cell during acquisition of the data. Wideband bit synchronizers or clock recovery schemes are discussed in the textbook entitled "Digital Communications by Satellite," by James J. Spilker, published by Prentice-Hall, Inc. in 1977, at pages 429-447. It should be emphasized that detection and clock recovery are considerably easier for wideband signals than narrowband signals. Bandlimiting severely distorts the signal waveform to complicate the detection process. Wideband signalling is usually used in communications link circuits where bandwidth is not at a premium (e.g., low-speed telephone data communications); narrowband signalling is utilized in bandwidth-sensitive communications.
As discussed above, the concept of sampling at the bit rate to correctly detect the data is dependent on correct clock recovery. The clock frequency and phase must be determined, for example from the received bit stream, and the data must be sampled at the clock frequency for accurate detection. When the data has been bandlimited, for instance to conserve link bandwidth, accurate clock recovery is further complicated. The problem of clock recovery is exacerbated when it is necessary for clock recovery to occur in a multi-rate environment. This problem arises when the receiving device (modem) is tunable to receive signals of various data rates. In this situation one encounters both the problem of recovering the clock in a narrowband or bandlimited environment and recovering clocks of various data rates without unnecessary hardware complexity.
FIG. 3 illustrates a prior art clock recovery circuit 19 for recovering the clock signal from a bandlimited binary information signal. The information signal is input to a bandpass filter 20 that has a center frequency f.sub.c =R/2, where R is the data rate. It is well-known to those skilled in the art that for a random or pseudo-random data stream (such as the bandlimited information signal) that there is a spectral line at R/2 that can be processed to extract the clock. It is also known that for any binary stream, either wideband or narrowband, there is no spectral line at the data rate R because the spectrum for a binary data stream is a sin x/x function with the first spectral null at the frequency R. The filtered signal is input to a frequency doubler 22, which is usually a square law circuit. The signal from the frequency doubler 22 is input to a narrow bandpass filter 24, which has center frequency 2f.sub.c equal to the data rate R. The narrow bandpass filter 24 is often implemented as a part of a phase-locked loop, but in the embodiment of FIG. 3 the narrow bandpass filter 24 is shown as a separate element from the phase-locked loop 26. The frequency spectrums for the signals generated in each of the elements of FIG. 3 are shown in FIGS. 4A, 4B, 4C, 4D and 4E. The alphabetical letter designations in FIG. 3 identify the associated frequency spectrum of FIG. 4. Other prior art clock recovery schemes similar to the FIG. 3 embodiment are discussed in the following references: W. R. Bennett, "Statistics of Regenerative Digital Transmission", Bell System Technical Journal, Volume 37, pp. 1501-1542, November 1958; Y. Takasaki, "Timing Extraction in Baseband Pulse Transmission", IEEE Transactions on Communications, Volume COM-20, pp. 877-884, October 1972; L. E. Franks and J. P. Bubrowski, "Statistical Properties of Timing Jitter in a PAM Timing Recovery System", IEEE Transactions on Communications, Volume COM-22, pp. 913-920, July 1974.
Although the FIG. 3 embodiment recovers the clock frequency for correct sampling of the information signal, it does not recover the clock phase. For fixed data rate modems clock phase recovery is often accomplished by generating an eye pattern on a cathode ray tube and placing a manual adjustment of the clock phase in series with a clock recovery circuit. This adjustment allows the operator to control the clock phase so that the clock signal appears in or near the middle of the eye pattern. Automatic clock phase control can be implemented by including a bit error rate counter in the receiving circuitry. The bit error rate is monitored and minimized by changing the clock phase. As an alternative to moving the clock to change the phase, it is possible to actually move the data. For instance, it is well known to use adaptive equalizers to move the data so that it is in phase synchronism with the clock. The end result is that the eye pattern is again positioned correctly over the top of the recovered clock.
In the multiple baud rate environment the problems of clock frequency and phase recovery are much more complex. If the clock frequency changes by a few percent the phase-locked loop 26 can track the frequency change. But for large data rate changes, for example from 20 MHz to 40 MHz, the prior art modems or receiving devices include a bank of bandpass filters, like the bandpass filter 20, one for each received data rate. A different bandpass filter is switched in the circuit in accord with the received data rate. This obviously raises the parts count and complexity of the hardware for multiple data rate modems.